Note: Descriptions are shown in the official language in which they were submitted.
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A THERMOMETER BASED ON CB TUNNELLING
The object of the invention is a thermometer based on CB
tunnelling, which comprises a sensor component and devices for
s measuring its voltage-current dependence, and in which the
sensor includes a chain of several, at least ten, nanoscale
tunnel junctions on a semiconductor base and connection
electrodes for connecting the measurement devices to the ends
of the chain, and in each tunnel junction the resistance is at
io least 10 kQ, and in which the temperature T is determined in a
way that is, as such, known, on the basis of the characteristic
quantities of the graph G/G, of the voltage/current dependence.
A thermometer based on the Coulomb blockade and its principles
15 has been described in the journals Physical Review Letters,
Vol. 73, No. 21, 21 Nov. 1994, pp. 2903 - 2906; Applied Physics
Letters, 67(14), 2 Oct. 1995, pp. 2096 - 2098; and Journal of
Low Temperature Physics, Vol. 101, Nos. 1/2, Oct. 1995, pp. 17
- 24. In the sensor of the thermometer there are several tunnel
20 junctions arranged as a sequential chain. The phenomenon known
as the Coulomb blockade causes a conductance drop at the zero
point of the bias voltage, the characteristic quantities of
which depend on the temperature. The method is based on the
/2C, where C is the
joint effect of the charging energy E, = e2
25 capacitance of the junction in question, of the very small
capacitor formed by the small metallic island isolated by the
tunnel junctions, and the thermal energy kBT. It becomes
apparent that when the voltage-current characteristic curve of
the chain of tunnel junctions is measured, more precisely as a
3o function of the voltage affecting its dynamic resistance over
tize tunnel junction, a zero-centre peak can be observed, the
widtn of which is directly proportional to the temperature, and
its absolute value corresponds to that calculated theoretically
w;t:n a very high degree of accuracy. This property makes the
-s thermometer a primary thermometer. On the other hand, the
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peak is in inverse proocrtion to the temperature,
_srn proviaes a secondary t::er^;ometer.
_-'mar_/ thermcmeters are rare, parc:cularly at low tempera-
_...res. Scme few in this category are the (ideal) gas thermome-
ter at a te*nperature of more than 3 K, the nuclear orientation
t:.er-ncmeter at temperatures of 3 - 50 mK, and the noise
thermcmeter. A thermometer based on C3-tunneling (CBT), offers
several advantages compared with those.
In practise, there are, however problems in CBT applications.
First, the total impedance of the sensor becomes very great. In
order that the theory can be realized in the tunnelling event
itself as accurately as possible, the resistance RT of each
is tunnel junction must be clearly greater than the quantum
resistance RK fii/e` a 4 kQ. In practice, RT 20 kQ has been
shown to be sufficient . On the other hand, in order that the
detrimental effect of the ends of the tunnel junction chain on
the operation of the sensor is minimized, there must be at
-.o least N a 20 junctions in the series. These two conditions
combined give a "good" sensor minimum impedance (resistive) of
Z-.,;; = 400 kQ. Such a high level of impedance causes problems,
especially if the distance between the sensor and the electron-
ics controlling it, and with it the capacitance of the measure-
:= ment leads, increase:
Secc%clv, the temperature range of the sensors should be
~r_ reased. The optimal temperature of the tunnel junction chain
determined by the capacitance C of the tunnel junctions. The
-~_. _=ature rance of a senscr can nowadavs be brought to
;ess t:.an two decades. The upper limit temperature is
~-_er...:.ned 'ay the sicr.al-ncise rat_o of the measurement, __.
__ =.acr~~ , the sma-_est measurab-e conductar.ce oeak. ':'he
te.^pz=at',..re ct eac-": sZn :cr _s -For its ;.art detp1_"-
CI1Cer Op e_at , as
i
_____ == _ _act that i:e se_.ser '.Ji_l no
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might be expected from the simple series development, if the
relative height of the peak grows so that AG/GT z 0,2.
Thirdly, a frequent problem at temperatures of less than 1 K is
the fact that the current flowing through the chain heats the
sensor, so that the electron temperature, which is being
measured here, rises above the temperature of the substrate.
A fourth type of a problem worth mentioning, is that particu-
lo larly relating to the present material, aluminium. First,
aluminium is a superconducting metal at temperatures of less
than 1K. Because the sensor only works as a normal metal, a
powerful magnetic field of about 0,5 T is required, by means of
which the aluminium can be kept normal at ever lower tempera-
is tures. Secondly, at temperatures greater than 50 K the limiting
factor becomes the height of the Al/AlOX/Al tunnel barrier,
which is about 2 eV.
The invention is intended to resolve the above problems. The
20 characteristic features of the invention are presented in the
accompanying Claims.
A thermometer according to the invention based on the Coulomb
blockade has the following advantages.
25 1. The operating temperature range of each tunnel junc-
tion array is about two orders at the temperature and
can be selected by making tunnel junctions of the
desired size: the smaller the junction, the higher the
temperature and vice versa. In practice, the smallest
30 junction size that has been achieved at present is
about 30 nm x 30 nm, which corresponds to a tempera-
ture range of 1 - 100 K. With a larger junction size
a temperature range of 0,05 - 4,2 K can be achieved.
Thus, the total temperature range of a sensor contain-
5 ing 2 - 3 arrays is 0,05 - 100 K.
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2. Even a powerful magnetic field does not affect the
operation and reading of the meter. This has been
investigated at fields of up to 8 T.
3. In resistance measurements, it is possible to exploit
the properties of the sensor as both a primary and
secondary meter. The result is a fast and reliable
device.
io 4. The manufacture of the sensor is based on modern
nanotechnology and is thus highly repeatable and is
suitable for even large numbers of sensors.
S. The sensor is very small.
In what follows, the invention is described with the aid of an
example, with reference to the accompanying illustrations.
Figure 1 shows the basic construction of a sensor consisting of
three arrays on a semi-conducting substrate, with
junction electrodes.
Figure 2 shows the circuit diagram of one CB tunnel junction
array.
Figure 3 shows tunnel junctions intended for different tempera-
ture ranges; formed on a silicon substrate, at the
same scale.
Figure 4 shows the structure of the lowest temperature range
tunnel junction chain, with the electron
thermalization areas in the conductors between the
junctions.
Fiaure 5 shows the structure of a single tunnel junction in
cross-section.
T~e example sensor comprises of tunnel junction arrays 4, 4',
and a" adapted to three different temperature ranges, which are
connected at one end to a common connecting electrode 2 and at
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the other end of each to its own connecting electrode 3, 3',
and 3", with the aid of connecting conductors 5. The sensor is
encased in the conventional manner of microcircuits, for
example as an 8-pin socket of a standard-size. The desired
5 array for measurement is selected by means of the measurement
electronics.
All three arrays are according to Figure 2. The measurement
connection on the negative side of the arrays is connected in
io the manner described above, but the positive sides are sepa-
rate. Array 4 of Figure 2 consists of 10 identical tunnel
junctions 4.1 ... 4.10 connected in parallel. If the resistance
of one chain is 400 kS2, the resistance of the entire array is
only 40 kS2, when the problems referred to above are avoided. At
its maximum, the total resistance may be at most 150 kQ. Most
advantageously, there are 4 or 5 chains in parallel, in which
case manufacture is not unreasonably difficult, but the
resistance of the array drops to less than 100 kQ.
Figure 3 shows diagrammatically the manner of varying the
geometry of the tunnel junction. The junction capacitance can
be most easily adjusted by varying the surface area of the
tunnel junction. The thickness of the thin oxide layer used as
insulation is the same over the entire base. In the upper part
of Figure 3 is a low temperature range tunnel junction 10",
with a surface area of about 1,5 m2. It arises with the aid of
an insulating layer between conductors 7" and 8". In the lower
part of Figure 3, there is a high temperature range tunnel
junction chain on the same scale. In this chain, too, there are
20 tunnel junctions in series, connected by conductors 7 and 8.
Tr.e surface area of each tunnel junction is less than 0,01 m2.
Due to the manufacturing technique used, separate sections of
a chain arise also on each side of the tunnel junction chain.
However, these play no part in the operation of the sensor.
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The tunnel junctions of the sensor are most advantageously
manufactured using electron beam lithography, which achieves a
much higher accuracy than when using photolithography.
At low temperatures, less than 1 K the measurement current
begins to disturb the measurement, as stated above. This
problem is resolved in the manner according to Figure 4, in
which the intermediate conductors 7 and 8 of the tunnel
junction 10 are spread out to become a large cooling area 13 at
io the sides. In these areas, which are thus of aluminium (or
similar) , the electrons can thermalize. Electrons thermalize
in the entire volume of the conductor and decelerate through
interaction with the environment. The increase in capacitance
is not detrimental. The substrate does not conduct in this
temperature range.
4 - 5 parallel chains equipped with cooling areas are a
suitable number, as a compromise between measurement and
manufacturing techniques.
Tunnel junction 10 and the conductors 7 and 8 that it requires
are formed on a pure silicon substrate 1, Figure S. For
practical reasons, an oxide layer i" is formed on the surface
of the basic material 1', so that the sensor can be tested at
room temperature. Using electron beam lithography, a conducting
layer 8, an insulating layer 9, and a second conducting layer
7 are formed in a sequence. The tunnel junction 10 is formed at
the junction between the conductors 7 and 8, where there is an
insulating layer about 1 nm thick between them. In the figure,
3o the thickness of the insulating layer 9 has been exaggerated.
The thickness of conductors 7 and 8 is actually about 100 nm.
The dynamic behaviour of a tunnel junction chain has been
described in the publications referred to above. It is possible
to der'-ve the following formulae from them for performing
measurement. The dimensionless conductance G/G. in,such a chain,
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in which there are N tunnel junctions with a capacitance of C,
can be approximately calculated from the formula
E
Gi GT = I ce Y/NkB7), in which
s
E = 2~N-1)e'-
~ N 2C
Primarily, the temperature T is determined, in a thermometer
based on CB tunnelling, on the basis of the descriptor G/GT from
the formula VK = 5,439 N kHT/e, in which V3j is the measured
voltage difference of the conductance drop at the drop side
depth, N is the number of tunnel junctions in the chain, kB is
the Boltzmann constant, and e is the unit charge. The measure-
io ment of the temperature thus returns to become the measurement
of the voltage. The determination of the full width at half
minimum of the conductance drop does not demand absolute
accuracy of the parameters, because it is determined on the
basis of the relative data of the sensor. After the determina-
is tion of the depth, the half value voltage values are sought at
on both sides of the drop, the difference is V. to be sought.
The temperature can also be obtained from the equation in a
secondary manner:
F.
OGrGT = ~ in which
6kBT~ .
OG/G- is the depth of the dimensionless conductance drop.
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To eliminate the drawbacks of aluminium, it may be replaced by
another metal, such as chromium Cr, copper Cu, nickel Ni, or
niobium Nb.
